B2039
Title: Distributional regression via optimal transport
Authors: Victor Panaretos - EPFL (Switzerland) [presenting]
Laya Ghodrati - EPFL (Switzerland)
Abstract: A framework is presented for performing regression when both covariate and response are probability distributions on a compact real interval. Our regression model is based on the theory of optimal transportation and links the conditional Frechet mean of the response distribution to the covariate distribution via an optimal transport map. We define a Frechet-least-squares estimator of this regression map, establish its consistency, and show it attains the minimax rate of convergence to the true map. The computation of the estimator is shown to reduce to an isotonic regression problem, and thus our regression model can be implemented with ease. We illustrate our methodology using real and simulated data.
